How to achieve anime-like smears in blender?
In node editor:
You could try using the displace node which moves each pixel according to an input rgb, where red is how much the pixels will move in the x direction, and green is how much pixels will move in the y direction.



(I didn't change any settings for the cloud texture, I just use the default values)

Edit: 

In 3d editor:
If you want to do it directly on a 3d model in the 3d view, you can use the displace modifier.


create a cloud texture and make the size very small.
Then add the first sub-surf modifier if your model don't have enough geometry.
Then add the displace modifier under, and change the direction to only 1 direction (X, Y or Z)
Then add 1 more sub-surf modifier to smooth things out.